General background of nuclear magnetic resonance (NMR) well logging is set forth, for example, in U.S. Pat. No. 5,023,551. Briefly, in conventional NMR operation, the spins of nuclei align themselves along an externally applied static magnetic field. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field (e.g. a radio frequency (RF) pulse), which tips the spins away from the static field direction. After tipping, two things occur simultaneously. First, the spins precess around the static field at the Larmor frequency, given by ω0=γ×B0, where B0 is the strength of the static field and γ is the gyromagnetic ratio. Second, the spins return to the equilibrium direction according to a decay time T1, which is called the longitudinal relaxation time constant or spin lattice relaxation time constant. For hydrogen nuclei, γ/2π=4258 Hz/Gauss, so, for example, for a static field of 235 Gauss, the frequency of precession would be 1 MHz. Also associated with the spin of molecular nuclei is a second relaxation time constant, T2, called the transverse relaxation time constant or spin-spin relaxation time constant. At the end of a ninety degree tipping pulse, all the spins are pointed in a common direction perpendicular to the static field, and they all precess at the Larmor frequency. The net precessing magnetization decays with a time constant T2 because the individual spins rotate at different rates and lose their common phase. At the molecular level, dephasing is caused by random motions of the spins. The magnetic fields of neighboring spins and nearby paramagnetic centers appear as randomly fluctuating magnetic fields to the spins in random motion. In an inhomogeneous field, spins at different locations precess at different rates. Therefore, in addition to the molecular spin-spin relaxation of fluids, spatial inhomogeneities of the applied field also cause dephasing. Spatial inhomogeneities in the field can be due to microscopic inhomogeneities in the magnetic susceptibility of rock grains or due to the macroscopic features of the magnet.
A widely used technique for acquiring NMR data, both in the laboratory and in well logging, uses an RF pulse sequence known as the CPMG (Carr-Purcell-Meiboom-Gill) sequence. As is well known, after a wait time that precedes each pulse sequence, a ninety degree pulse causes the spins to start precessing. Then a one-hundred-eighty degree pulse is applied to cause the spins which are dephasing in the transverse plane to refocus. By repeatedly refocusing the spins using one-hundred-eighty-degree pulses, a series of “spin echoes” appear, and the train of echoes is measured and processed. The transverse relaxation time constant, T2, or the distribution of multiple T2s, can be obtained using this technique. In well logging, the CPMG sequence is traditionally executed using a set of equipment located “down-hole” in a well bore (in situ). While performing the CPMG sequence in situ allows for relatively rapid data gathering, limitations of the equipment and the environment can make it difficult to obtain accurate down-hole data. For example, due to the limits on equipment power, design constraints and down-hole conditions, the signal to noise ratio (SNR) for an in situ CPMG sequence remains low. This low SNR can impede the gathering and analysis of useful data about the formation in the ground.